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The coupling in integrated electricity and gas community energy system (IEGS) provides alternative operation modes when unpredictable outages occur at energy-supply sides. Reasonable operation strategies and system configuration can effectively improve the system's resilience, making reliable and continuous operation feasible. Based on the complementary characteristics and reserve capabilities of IEGS, this paper proposes a multi-stage scheduling strategy for resilience enhancement in which thermal storage serves as emergency response resources. The resilient scheduling framework consists of rolling reserve optimization stage, day-ahead economic dispatch stage and fault restoration stage. With the reserve capacity of energy storage generated by rolling optimization and day-ahead dispatch, multiple forms' critical loads will be satisfied in priority when outage occurs on energy-supply sides. Furthermore, a two-level planning model integrating the resilient operation strategy is formulated to better adapt to the source emergency. The proposed planning method is applied to an IEGS with practical demands as a case study. The results show that the configuration generated by the two-level planning model can satisfy the daily reserve requirements for emergency failures, and the resilient scheduling strategy with storage reserve can improve the system resilience effectively.